Question

Part: 1

The width of a rectangle is 13 its length, l.

Which expression represents the perimeter of the rectangle?

1/3 L+L

2(L+1/3L)

4×1/3L

4(l+1/3L)

Part 2

The perimeter of the rectangle from Part 1 is 56 inches.

What is the area of the rectangle, in square inches?

____________________square inches

Answer 1

Part 1:
perimeter = 2(Length + width)
if the width is 1/3 it's length, then
width = 1/3L
plug that into the first equation
perimeter = 2( L + 1/3L)

Part 2:
the perimeter of the rectangle from part 1 is 56 inches. using this we can solve for L, the length:
56 = 2(L + 1/3 L)
56 = 2L + 2/3L
56 = 2 2/3 L
L = 21

Now that we know the length, we can solve for the width.
L = 21
W = 1/3 L
W = 1/3 x 21
W = 7

Using the Length (21 inches) and the Width (7 inches), we can solve for the area of the rectangle.
Area = length x width
Area = 21 inches x 7 inches
Area = 147 square inches